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- W3206958026 abstract "Various authors have been generalizing some unital ring properties to nonunital rings. We consider properties related to cancellation of modules (being unit-regular, having stable range one, being directly finite, exchange, or clean) and their “local” versions. We explore their relationships and extend the defined concepts to graded rings. With graded clean and graded exchange rings suitably defined, we study how these properties behave under the formation of graded matrix rings. We exhibit properties of a graph E which are equivalent to the unital Leavitt path algebra [Formula: see text] being graded clean. We also exhibit some graph properties which are necessary and some which are sufficient for [Formula: see text] to be graded exchange." @default.
- W3206958026 created "2021-10-25" @default.
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- W3206958026 date "2021-11-22" @default.
- W3206958026 modified "2023-10-16" @default.
- W3206958026 title "Cancellation properties of graded and nonunital rings. Graded clean and graded exchange Leavitt path algebras" @default.
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- W3206958026 doi "https://doi.org/10.1142/s0219498823500500" @default.
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